Weight optimized pressurizable aircraft fuselage structures having near elliptical cross sections

ABSTRACT

An aircraft fuselage includes a tubular shell having a centerline axis, opposite ends, and a cross-section having a radius R(φ), where φ is the angular coordinate of a cylindrical coordinate system, a curvature Curv(φ), where Curv(φ) is the inverse of a local radius of curvature of a surface of the shell, and a circumferential shape that varies radially by no more than ±7% from that of an elliptical cross-section at substantially every station along the centerline axis between the nose and tail ends thereof. The weight of the shell is minimized by “tailoring,” i.e., optimizing, at least one structural attribute, expressed as a function of φ, associated with every element of the shell, such that the weight of the shell required to react a design load incident thereon is less than that required to react the same design load, but wherein the same structural attribute has not been so tailored.

TECHNICAL FIELD

This invention relates to aircraft design in general, and in particular,to the design of a lightweight structure for a pressurizable aircraftfuselage having an elliptical or near-elliptical cross-section.

BACKGROUND

Certain classes of internally pressurizable aircraft fuselages, such aspassenger planes, can beneficially employ near-ellipticalcross-sections. For example, U.S. Pat. No. 6,834,833 to M. K. V.Sankrithi discloses the use of an aircraft having a fuselage 10 with aquasi-elliptical, or near-elliptical cross-section that is wider than itis tall. Representative front-end and a top plan cross-sectional viewsof this class of fuselage shape are illustrated in FIGS. 1A and 1B,respectively, wherein the fuselage comprises a rigid, light weight shell12 having respective opposite, closed nose and tail ends 14 and 16. Thiscross-section efficiently encloses a main deck cabin 18, typicallyprovisioned as a spacious and comfortable twin-aisle, seven-abreastcabin, together with a cargo container 14 (typically a LD-3-46W orsimilar, standardized type of container) in a lower deck hold 20. Thistwin-aisle fuselage cross-sectional shape has also been shown to providea perimeter-per-seat ratio comparable to that of a correspondingsingle-aisle, six-abreast, conventional aircraft fuselage having acircular or blended circular arc cross-section, and consequently, canalso provide a cross-section-parasite-drag-per-seat ratio and anempty-weight-per-seat ratio that, in a zeroth-order analysis, arecomparable to those of the corresponding single-aisle fuselagecross-section, while offering better passenger comfort and owner revenueoptions.

However, achieving an optimized, lightweight structure for suchnear-elliptical cross-section fuselages presents a substantialengineering design challenge because of the structural and weightpenalties involved in moving from a fuselage design having aconventional circular cross-section to a fuselage design having anon-circular cross-section, especially those penalties that areassociated with pressurization effects inherent in the design ofhigh-altitude jet airliners.

Accordingly, there is a need in the aviation industry for design methodsand techniques for achieving lightweight structures for pressurizableaircraft fuselages having an elliptical or a near-ellipticalcross-section.

BRIEF SUMMARY

In accordance with the various exemplary embodiments thereof describedherein, the present invention provides an internally pressurizablefuselage structure for an aircraft having a near-elliptical shape and aweight that is minimized by “tailoring,” i.e., optimizing, thestructural attributes of substantially every element of the fuselage,expressed as a function of the angular coordinate φ of a cylindricalcoordinate system of the fuselage, to react, i.e., to sustain withoutfailure, all design loads incident thereon.

In a preferred exemplary embodiment thereof, the fuselage structurecomprises an elongated tubular shell having a central axis x, oppositeclosed nose and tail ends, and a non-circular cross-section having aradius R(φ) at substantially every point along the x axis between thetwo ends, where φ is the cylindrical angular coordinate, i.e., a rollelevation angle of the shell, that varies from 0 degrees to +360 degreesabout the x axis. The radius R(φ) of each cross-section of the shell isconstrained to vary radially by no more than ±7% from a radius r(φ) of atrue elliptical cross-section having a major axis of dimension 2·r_(max)and a minor axis of dimension 2·r_(min), and where r(φ) is given by therelation:${r(\varphi)} = {\frac{r_{\min}}{\sqrt{\left\lbrack {\left( {\left( {r_{\min}/r_{\max}} \right)^{2} \cdot \left( {\cos\quad\varphi} \right)^{2}} \right) + \left( {\sin\quad\varphi} \right)^{2}} \right\rbrack}}.}$

In the preferred embodiment, the maximum width of the shell exceeds themaximum height thereof, and the maximum width and height of the shellare respectively substantially aligned with the major and minor axes ofthe true elliptical cross-section. A curvature, Curv(φ), defined as theinverse of the local radius of curvature of a surface of the shell, isassociated with R(φ), and a corresponding curvature κ(φ) associated withr(φ) of the true elliptical cross-section is given by:${\kappa(\varphi)} = {\frac{\left\lbrack {r^{2} + {2 \cdot \left( \frac{\partial r}{\partial\varphi} \right)^{2}} - {r \cdot \frac{\partial^{2}r}{\partial\varphi^{2}}}} \right\rbrack}{\left\lbrack {r^{2} + \left( \frac{\partial r}{\partial\varphi} \right)^{2}} \right\rbrack^{1.5}}.}$

The exemplary shell has at least one structural attribute associatedwith every cross-sectional element thereof that has been tailored as afunction of the elevation angle φ such that the weight of the shellrequired to react the design loads incident on that element is less thanthat required to react the same design load, but wherein the at leastone structural attribute has not been so tailored. In a preferredembodiment, the function of φ consists of either R(φ) or Curv(φ). Thus,an exemplary embodiment of a method for weight-optimizing, i.e.,minimizing the weight of, the fuselage comprises defining at least onestructural attribute of every circumferential element of the shell as afunction of either R(φ) or Curv(φ), i.e., as a “functional,” and thentailoring the at least one structural attribute of the element such thatthe weight of the shell required to react all design loads incident oneach circumferential element thereof is less than that required to reactthe same design loads acting thereon, but wherein the at least onestructural attribute has not been so tailored.

Advantageously, the shell of the fuselage can function as a pressurevessel in which the design loads of major interest include internalpressurization loads. The shell can comprise a circumferential outerskin and circumferentially spaced longitudinal stringers, disposedadjacent to an inner surface of the skin, and the at least one tailoredstructural attribute can comprise at least one of a cross-sectionalshape and size, number, and material of the stringers. Each of at leastone of the circumferential skin and the stringers can comprise a“composite” of a plurality of plies, each having a selected angularorientation relative to the others, the at least one tailored structuralattribute can comprise at least one of the number, relative angularorientation, and material of the plies.

Alternatively, the shell can comprise a “sandwich” structure, i.e.,circumferential outer and inner skins attached to a rigid core, whichcan comprise either of a continuous rigid foam or of interconnectedcells, and the at least one tailored structural attribute can compriseat least one of a thickness of the core, a core density or core celldensity and a core material. The skins can be made from eitherthermosetting or thermoplastic material, and by hand lay up, machine layup or resin infused.

In another embodiment, the shell can comprise an “isogrid” structurehaving at least one external face sheet attached to a grid comprisinginternal stiffening members, and the at least one tailored structuralattribute can comprise at least one of grid spacing, grid geometry, gridmaterial and face sheet material.

In still yet another embodiment, the shell can comprise a filament-woundstructure in which the at least one tailored structural attribute mayinclude the filament cross-sectional shape and size, winding pitch,and/or the number of fibers in the filament.

A better understanding of the above and many other features andadvantages of the present invention may be obtained from a considerationof the detailed description of the exemplary embodiments thereof below,particularly if such consideration is made in conjunction with theappended drawings, wherein like reference numerals are used to identifylike elements illustrated in one or more of the figures therein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are cross-sectional front end and top plan views,respectively, of an internally pressurizable aircraft fuselage inaccordance with the prior art;

FIGS. 2A and 2B are cross-sectional front end and top plan views,respectively, of an exemplary embodiment of an internally pressurizableaircraft fuselage in accordance with the present invention;

FIG. 3 is a representative cross-sectional diagram of the fuselage ofFIG. 2, as expressed in a cylindrical coordinate system;

FIG. 4 is a representative diagram of an exemplary embodiment ofstructural components of the fuselage of FIG. 2, as expressed in acylindrical coordinate system and mapped onto a two-dimensional plane,showing a stringer-frame type of fuselage architecture;

FIGS. 5A-5D are plan views of alternative embodiments of structuralcomponents of the fuselage of FIG. 2, showing exemplary embodiments ofcore cells of a composite-sandwich fuselage architecture;

FIGS. 6A-6G are plan views of alternative embodiments of structuralcomponents of the fuselage of FIG. 2, showing exemplary embodiments ofgrids of a composite Isogrid fuselage architecture;

FIG. 7 illustrates an exemplary tailoring function of a structuralattribute; and,

FIG. 8 is a schematic plan view of a fuselage structure showingexemplary ply orientations.

DETAILED DESCRIPTION

FIGS. 1A and 1B respectively illustrate cross-sectional front end andplan views of a prior art pressurizable aircraft fuselage 10 having apassenger cabin 18 and a cargo compartment 20. This invention provides alightweight fuselage shell structure for such an aircraft in which theshell has a near-elliptical cross-section by applying “tailoring,” i.e.,optimally selected adjustments, of the structure to more closely matchcritical design loads as a function of the roll elevation angle φmeasured around the centerline axis of the cross-section. An exemplaryembodiment of a fuselage shell 20 having a near-elliptical cross-sectionin accordance with the present invention is illustrated in the front-endcross-sectional view of FIG. 2A. In FIG. 2A, the periphery or outerperiphery of the shell is designated 28, and a window belt 31 isdisposed adjacent to a passenger cabin 22 having a main cabin floor 32.A cargo compartment 26 is shown with a Unit Load Device or cargocontainer 24. A crown region 27 and a keel region 29 of the shell definethe upper and lower extremities of the shell.

For the purposes of this invention, the term “near-ellipticalcross-section” should be understood as a cross-section that isapproximately elliptical in shape, with a width-to-height (orheight-to-width) ratio that is between 1.01 and 1.30, and with across-sectional periphery, or circumference, that is either a “pure”ellipse, i.e., strictly elliptical in shape, or that is between ±7% fromsuch a strictly elliptical shape, as measured in a direction extendingradially outward from the centerline axis of the fuselage shellcross-section, at substantially every point, or longitudinal station,along the central axis thereof.

FIG. 2B illustrates a plan view of the embodiment of FIG. 2A, showing anelongated, internally pressurizable tubular shell 21 and opposite closednose and tail ends 23 and 25, as well as means for lifting 13 (e.g.,wings) the shell off the ground and for propelling 15 (e.g., engines) itrelative to the ground.

As illustrated schematically in FIG. 3, for purposes of description, acylindrical coordinate system is assumed, with x positive forwardsubstantially along the longitudinal, or centerline axis of the fuselageshell 30; where the radius r is positive radially outward from the xaxis, and the angular coordinate φ is positive rotating upward from φ=0from a substantially horizontal vector pointing to the right of theaircraft, looking forward, at right angles to the x axis. Thus, it maybe seen that the cylindrical angular coordinate φ corresponds to a “rollelevation angle” of the shell that varies from 0 degrees to +360 degreesabout the x axis. The corresponding Cartesian coordinate system has anx-axis that is positive forward along the centerline axis of thefuselage shell cross-section, a y axis that is positive to the left sideof the centerline axis of the aircraft, and a z axis that is positiveupwards from the centerline axis, as illustrated in FIG. 3.

If the nominal shape of the periphery or circumferential perimeter 38 ofthe cross-section of the aircraft's fuselage shell 30 is that of a“true” ellipse, as shown by the phantom outline of FIG. 3, i.e., onehaving a substantially horizontal major axis of diameter D_(maj) (width)equal to 2·r_(max) and a substantially vertical minor axis with adiameter D_(min) (height) equal to 2·r_(min), and with an eccentricity egiven by${e = \sqrt{\left( {1 - \left( {r_{\min}/r_{\max}} \right)^{2}} \right)}},$then the radius r, expressed as a function of φ, is given by${{r(\varphi)} = \frac{D_{\min}}{2 \cdot \sqrt{\left\lbrack {\left( {\left( {r_{\max}/r_{\min}} \right)^{2} \cdot \left( {\cos\quad\varphi} \right)^{2}} \right) + \left( {\sin\quad\varphi} \right)^{2}} \right\rbrack}}},$or, by defining A=(r_(min)/r_(maj))=(D_(min)/D_(maj)), by${r(\varphi)} = {\frac{D_{\min}}{2 \cdot \sqrt{\left( {\left( {{A^{2} \cdot \cos^{2}}\varphi} \right) + {\sin^{2}\varphi}} \right)}}.}$

A “curvature,” κ(φ), defined as the inverse of the local radius ofcurvature for the surface, is given for the true elliptical shape 38 bythe following equation:${\kappa(\varphi)} = {\frac{\left\lbrack {r^{2} + {2 \cdot \left( \frac{\partial r}{\partial\varphi} \right)^{2}} - {r \cdot \frac{\partial^{2}r}{\partial\varphi^{2}}}} \right\rbrack}{\left\lbrack {r^{2} + \left( \frac{\partial r}{\partial\varphi} \right)^{2}} \right\rbrack^{1.5}}.}$

However, if the nominal cross-sectional outer surface or perimeter 38 ofthe shell 30 is not a true ellipse, but rather, a near-ellipse, asdescribed above, the equations for the local radius and curvature arenot exactly as stated above, but instead, result in slightly differentequations, or more practically, can comprise digitally specified curvesthat are amenable to digital computer modeling techniques. Thus, forpurposes of this invention, a fuselage shell 30 is considered to have anear-elliptical cross-sectional shape when its radius function R(φ)varies radially by no more than ±7% from a radius r(φ) of a trueelliptical cross-section r(φ), as illustrated in FIG. 3. Likewise, thelocal curvature of the near-ellipse, defined herein as “Curv(φ),” maydiffer correspondingly from the curvature κ(φ) of the pure ellipticalshape, and still be deemed to have a near-elliptical cross-sectionalshape in accordance with the invention.

As those of skill in the art will appreciate, the distribution ofcritical design loads around the circumferential perimeter 38 of afuselage shell 30 having a near-elliptical cross-section may vary atdifferent longitudinal fuselage locations, or stations, depending notonly on pressurization-induced loads, but also on combinations of suchpressurization loads with other fuselage bending and torsional loads,for example, those resulting from horizontal and vertical tail-maneuverrelated loads, or wind gust loads, and critical design loads may furtherbe driven by compression, tension, shear and buckling considerations inselected parts of the fuselage structure, as well as minimum materialgauge or thickness considerations, barely visible impact damage (BVID)criteria for potential damage by hail or other impacts, and fatigueand/or aeroelastic design considerations and criteria.

It may be further appreciated that achieving an optimized, lightweightstructure, or shell, for such near-elliptical cross-section fuselagespresents a design challenge because of the structural and weightpenalties involved in implementing a design having a non-circularcross-section, especially those associated with pressurization effects.However, it is has been discovered that it is possible to achieve aweight-optimized near-elliptical fuselage shell in accordance with themethod described below.

Initially, it should be understood that the exemplary shell 30 has atleast one structural attribute associated with every circumferentialelement of every cross-section thereof that can be tailored as afunction of the elevation angle φ such that the weight of the shellrequired to react a design load acting thereon, including any safetyfactor desired, is less than the weight of an identical shell necessaryto react the same design load, but in which same elemental structuralattribute has not been so tailored. In one preferred embodiment, thefunction of φ comprises either R(φ), Curv(φ) or a combination thereof.Thus, an exemplary embodiment of a method for minimizing the weight ofthe fuselage shell 30 comprises defining at least one structuralattribute of every circumferential element of every cross-section of theshell as a function of either R(φ), Curv(φ), or a combination thereof,i.e., as a functional, and then tailoring the at least one structuralattribute of the element such that the weight of the shell required toreact all design loads incident on each element thereof is less thanthat required to react the same design loads incident thereon, butwherein the at least one structural attribute has not been so tailored.

FIG. 4 schematically illustrates a representative “skin-stringer”geometry used in typical aircraft fuselage shell architecture, shown asif cut open longitudinally and laid out flat, or “mapped,” onto atwo-dimensional plane having an abscissa parallel to the centerline axisx of the shell, and an ordinate corresponding to a circumferentialdistance l_(c) from the abscissa (see FIG. 3), in which the structuralcomponents of the shell comprise at least an outer circumferential skin40, or “aeroskin,” attached to a generally orthogonal grid structurethat includes a plurality of circumferentially spaced longitudinal“stringers” 42 disposed generally parallel to each other and thelongitudinal x-axis of the shell, and a plurality of longitudinallyspaced formers, or “frames” 44, disposed generally parallel to eachother and orthogonal to the stringers. The frames may includecircumferential flanges 46 and radial webs 48.

In accordance with the present invention, the weight-optimization, ortailoring, of the structure for a skin-stringer fuselage architecturesuch as that illustrated in FIG. 4 can include one or more of tailoringthe associated structural attributes, in terms of φ, of: The gauge, orthickness of, the skin 40; the radial depth of the frames 42; thethickness of the respective frame flanges 46; the thickness of therespective frame webs 48; and, tailoring of the attribute as a functionof φ and stringer 42 cross-sectional shape and/or size (e.g.,“hat-shaped”, “F”, “T”, “L” shaped, etc.), plus the type of material,e.g., a metal, such as aluminum, or a non-metal, e.g., carbon fibersembedded in specified orientations, patterns and layers, in a resinmatrix, from which each of these structural components are formed.

For so-called “composite-body” skins 40, the structural attributes canbe tailored as a function of φ and, e.g., the number of plies, orlayers, in the skin, and/or the relative angular orientation angle ofthe plies to each other, and/or a percentage distribution, byorientation angle, of the plies provided at that particular φ. The skinscan also be tailored in terms of variations in the types and quantitiesof materials (i.e., composite, metallic, or a combination thereof) usedtherein as a function of φ.

As is known, composite-body aircraft fuselage shells can advantageouslyincorporate skins comprising composite “sandwiches,” i.e., stiff,lightweight “core” structures 50 comprising either a continuous foam orhoneycomb cells 52 laminated between two circumferential skins, or facesheets. Representative core cell geometries are illustrated in FIGS.5A-5D, where it should be understood that the cores are sandwichedbetween inner and outer face sheets (not illustrated).

Such tailoring of fuselage shell structural attributes as a function φand one or more other variables can also be advantageously applied toother structural components of sandwich composite structures, includingthe skins thereof, i.e., tailoring as a function of φ and inner andouter face sheet properties, including the number of plies therein,respective ply relative and/absolute orientation angles, and/orpercentage distribution by orientation angle of the plies provided atthat particular value of φ, as well tailoring in terms of φ of sandwichcore thickness, and/or cell density, core material and/orsandwich-specific localized design and construction. Thus, for example,the core material can be tailored throughout the design process byvarying, e.g., core material, type and density.

Tailoring of fuselage structural attributes as a function of φ can alsobe effected in the context of so-called “isogrid” structures. An isogridpanel comprises at least an external skin, or face sheet, as above, withintegral stiffening or stringer members 60 that are arranged in patternsof cells 62, as illustrated in FIGS. 6A-6G, and is amenable to analysisusing known isogrid plate modeling techniques. (See, e.g., Meyer, R., etal., Isogrid Design Handbook, NASA Center for Aerospace Information(CASI), NASA-CR-120475; MDC-G4295A, Feb. 1, 1973.) In the case of anaircraft fuselage shell, such isogrid structures can comprise a facesheet and integral stringer members that, in the case of composite-bodystructures as described above, can be laid up together by, for example,known fiber placement or filament winding techniques. Tailoring of thestructural attributes of isogrid structures as a function of φ can beeffected for isogrid structures in a manner similar to isogrid designand construction attributes that vary as a function of φ. This caninclude grid type, shape, spacing and material utilization, includingmixing material types for both the grid face sheets and the isogridintegral stringer members.

FIG. 7 illustrates an exemplary tailoring function of a structuralattribute plotted as a function of φ. This type of exemplary function isrepresentative of when the structural attribute is linearly ormonotonically increasing with increasing [|R(φ)- R|] or [|Curv(φ)-Curv|]. The structural attribute could be skin gage, frame depth, orother structural attribute. If the structural attribute is frame depth,local frame depth in a crown region (i.e., φ near 90°) is increasedrelative to average frame depth, and local frame depth in a keel region(φ near 270°) is also increased relative to average frame depth. Itshould be understood that the tailoring function shown in FIG. 7 is onlyexemplary, and that airplane-specific tailoring functions can differ inshape, character and magnitude as needed to minimize weight and drag forapplicable loads.

FIG. 8 illustrates a plan view illustrating representative compositefiber ply orientations, including zero degree plies 81, ninety degreeplies 82, and plus and minus forty-five degree plies 83.

By now, those of skill in this art will appreciate that manymodifications, substitutions and variations can be made in and to thematerials, apparatus, configurations and methods of implementing andweight optimization of the near-elliptical aircraft fuselage structuresof the present invention without departing from its spirit and scope.Accordingly, the scope of the present invention should not be limited tothe particular embodiments illustrated and described herein, as they aremerely exemplary in nature, but rather, should be fully commensuratewith that of the claims appended hereafter and their functionalequivalents.

1. An internally pressurizable aircraft fuselage structure, comprising:an elongated tubular shell having a centerline axis x, opposite closednose and tail ends, and a non-circular cross-section having a radiusR(φ) at substantially every point along the x axis between the two ends,where φ is a roll elevation angle varying from 0 degrees to +360 degreesabout the x axis; and, wherein the radius R(φ) of each cross-section ofthe shell varies radially by no more than ±7% from a radius r(φ) of anelliptical cross-section having a major axis with a dimension of2·r_(max) and a minor axis with a dimension of 2·r_(min).
 2. Thefuselage structure of claim 1, wherein: a maximum width of the shell isgreater than a maximum height thereof; and, the maximum width and heightof the shell are respectively substantially aligned with the major andminor axes of the elliptical cross-section.
 3. The fuselage structure ofclaim 1, wherein r(φ) is given by the relation:${r(\varphi)} = {\frac{r_{\min}}{\sqrt{\left\lbrack {\left( {\left( {r_{\min}/r_{\max}} \right)^{2} \cdot \left( {\cos\quad\varphi} \right)^{2}} \right) + \left( {\sin\quad\varphi} \right)^{2}} \right\rbrack}}.}$4. The fuselage structure of claim 1, wherein a curvature Curv(φ),defined as the inverse of the local radius of curvature of a surface ofthe shell, is associated with R(φ), and a corresponding curvature κ(φ)associated with r(φ) is given by:${\kappa(\varphi)} = {\frac{\left\lbrack {r^{2} + {2 \cdot \left( \frac{\partial r}{\partial\varphi} \right)^{2}} - {r \cdot \frac{\partial^{2}r}{\partial\varphi^{2}}}} \right\rbrack}{\left\lbrack {r^{2} + \left( \frac{\partial r}{\partial\varphi} \right)^{2}} \right\rbrack^{1.5}}.}$5. The fuselage structure of claim 1, wherein: the shell has at leastone structural attribute that has been tailored as a function of theelevation angle φ such that the weight of the shell required to react adesign load incident thereon is less than that required to react thesame design load, but wherein the at least one structural attribute hasnot been so tailored.
 6. The fuselage structure of claim 5, wherein theshell functions as a pressure vessel, and wherein the design loadcomprises internal pressurization loads.
 7. The fuselage structure ofclaim 1, wherein the shell includes structural components comprising oneof: at least one external circumferential skin attached to internallongitudinal stringers and axially spaced circumferential frames; anexternal circumferential skin and an inner skin laminated to internalcore structures; and, an isogrid structure having at least one externalcircumferential skin attached to stiffening members arranged in a gridpattern.
 8. The fuselage structure of claim 7, wherein at least onedimension of at least one of the structural components is tailored as afunction of at least one of R(φ) and Curv(φ).
 9. The fuselage structureof claim 8, wherein the at least one dimension comprises a radialdimension, an axial dimension or a circumferential dimension.
 10. Thefuselage structure of claim 8, wherein the at least one dimensioncomprises a thickness of the circumferential skin.
 11. A method forminimizing the weight of a pressurizable aircraft fuselage of a typecomprising an elongated tubular shell having a central axis x, oppositenose and tail ends, and a non-circular cross-section having a radiusR(φ) at substantially every point along the x axis between the two ends,wherein: φ is a roll elevation angle of the shell varying from 0 degreesto +360 degrees about the x axis; R(φ) varies radially by no more than±7% from a radius r(φ) of an elliptical cross-section having a majoraxis of dimension 2·r_(max) and a minor axis of 2·r_(min), a curvatureCurv(φ) is defined as the inverse of the local radius of curvature of asurface of the shell and is associated with R(φ), and a curvature κ(φ)associated with r(φ) is given by:${{\kappa(\varphi)} = \frac{\left\lbrack {r^{2} + {2 \cdot \left( \frac{\partial r}{\partial\varphi} \right)^{2}} - {r \cdot \frac{\partial^{2}r}{\partial\varphi^{2}}}} \right\rbrack}{\left\lbrack {r^{2} + \left( \frac{\partial r}{\partial\varphi} \right)^{2}} \right\rbrack^{1.5}}};$the method comprising: defining at least one structural attribute of theshell as a function of the elevation angle φ; and, tailoring the atleast one structural attribute of the shell such that the weight of theshell required to react a design load incident thereon is less than thatrequired to react the same design load, but wherein the at least onestructural attribute has not been so tailored.
 12. The method of claim11, wherein: the shell comprises a circumferential skin having athickness; and, tailoring the at least one structural attributecomprises tailoring the thickness of the skin substantially as afunction of at least one of R(φ) and Curv (φ).
 13. The method of claim12, wherein: the circumferential skin comprises a multiply compositestructure made of at least one of non-metallic and metallic materials;each ply is oriented at a selected angle relative to the other plies;and, tailoring the at least one structural attribute comprises tailoringthe plies with respect to at least one of the number of plies, theangular orientation of at least one of the plies, and the material ofthe plies.
 14. The method of claim 11, wherein: the shell comprises aplurality of generally parallel, longitudinally spaced circumferentialframes; and, tailoring the at least one structural attribute comprisestailoring a radial depth of the frames substantially as a function of atleast one of R(φ) and Curv (φ).
 15. The method of claim 14, wherein:each circumferential flange comprises at least one of an inner and anouter circumferential flange; and, tailoring the at least one structuralattribute comprises tailoring a radial depth of the flange substantiallyas a function of at least one of R(φ) and Curv (φ).
 16. The method ofclaim 14, wherein: each circumferential flange comprises a radial web;and, tailoring the at least one structural attribute comprises tailoringa longitudinal thickness of the web substantially as a function of atleast one of R(φ) and Curv (φ).
 17. The method of claim 16, wherein: thelongitudinal thicknesses of the webs are variable in a radial direction;and, tailoring the at least one structural attribute comprises tailoringthe radial distribution of the web thicknesses substantially as afunction of at least one of R(φ) and Curv (φ).
 18. The method of claim14, wherein: each circumferential flange comprises a multi-ply compositestructure made of at least one of non-metallic and metallic materials;each ply is oriented at a selected angular orientation relative to theother plies; and, tailoring the at least one structural attributecomprises tailoring the plies with respect to at least one of the numberof plies, the relative angular orientation of the plies, and thematerial of the plies.
 19. An aircraft, comprising: a fuselage,including an elongated internally pressurizable tubular shell having acenterline axis, opposite closed nose and tail ends, and anear-elliptical cross-section having a radius R(φ), where φ is theangular coordinate of a cylindrical coordinate system concentric withthe centerline axis, a curvature Curv(φ), where Curv(φ) is the inverseof a local radius of curvature of a surface of the shell, and acircumference that varies radially by no more than ±7% from thecircumference of an elliptical cross-section at substantially everyposition along the centerline axis between the nose and tail endsthereof; and, means for lifting the fuselage off the ground andpropelling it in at least a forward direction relative to the ground.20. The aircraft of claim 19, wherein substantially every element of thecircumference of substantially each of the cross-sections of the shell,expressed as a function of φ consisting of at least one of R(φ) andCurv(φ), has at least one associated structural attribute that has beentailored as a function of φ such that the weight of the shell requiredto react a design load incident thereon is less than that required toreact the same design load, but wherein the at least one structuralattribute has not been so tailored.
 21. The aircraft of claim 20,wherein: the shell comprises a circumferential outer skin andcircumferentially spaced longitudinal stringers disposed adjacent to aninner surface of the skin; and, the at least one tailored structuralattribute comprises at least one of a cross-sectional shape and size,number, and material of the stringers.
 22. The aircraft of claim 20,wherein: each of at least one of the circumferential skin and thestringers comprises a composite of a plurality of plies, each having aselected angular orientation relative to the others; and, the at leastone tailored structural attribute comprises at least one of the number,relative angular orientation, and material of the plies.
 23. Theaircraft of claim 20, wherein: the shell comprises a circumferentialouter skin attached to a rigid core of at least one of a foam materialand a plurality of rigid, interconnected cells; and, the at least onetailored structural attribute comprises at least one of a thickness ofthe core, a core cell density and a core material.
 24. The aircraft ofclaim 20, wherein: the shell comprises an isogrid structure having atleast one external face sheet attached to a grid comprising internalstiffening members; and, the at least one tailored structural attributecomprises at least one of grid spacing, grid geometry, grid material andface sheet material.
 25. The aircraft of claim 19, wherein the shellcomprises a filament-wound structure.
 26. The aircraft of claim 19,wherein the shell comprises a tape-laid composite structure.
 27. Theaircraft of claim 19, wherein the shell comprises at least one of anautoclave-cured composite structure, a microwave-cured compositestructure and an E-beam cured composite structure.
 28. The aircraft ofclaim 19, wherein the shell includes at least one of acarbon-fiber-in-resin composite structure and a combination of compositeand metallic materials.
 29. The aircraft of claim 19, wherein the shellincludes at least one of stitched multiply composite structure, astitched resin-film-infused (RFI) composite structure and a stapledmultiply composite structure.
 30. The aircraft of claim 19, wherein theshell comprises a composite structure including electrically conductiveelements for mitigating at least one of electromagnetic effects (EME)and lightning effects acting upon the aircraft.
 31. The aircraft ofclaim 19, wherein the shell comprises a composite structure having anouter surface with a colored, electrically conductive riblet filmdisposed thereon for providing a decorative color, reduced aerodynamicdrag, and mitigation of lightning and electromagnetic effects (EME)acting the aircraft.
 32. The aircraft of claim 19, wherein the shellcomprises a composite skin having some longitudinally oriented fiberplies having an orientation of zero degrees, plus or minus 20 degrees,relative to a local fuselage surface axis system, and other plies woundcircumferentially around the shell and having orientations varyingwithin a range of 90 degrees, plus or minus 20 degrees, relative to thelocal fuselage surface axis system.
 33. The aircraft of claim 32,wherein the shell further comprises first angled plies havingorientations varying within a range of +45 degrees, plus or minus 20degrees, relative to the local fuselage surface axis system, and secondangled plies with orientations varying within in a range of −45 degrees,plus or minus 20 degrees, relative the local fuselage surface axissystem.
 34. The aircraft of claim 33, wherein the first angled plies andthe second angled plies are laid down around the shell during itsconstruction along steered paths such that the magnitude of theirrespective orientations exceeds 45 degrees for regions of φ whereincircumferential loads incident on the shell exceed longitudinal loadsincident thereon by a selected amount.
 35. The aircraft of claim 33,wherein the first angled and second angled plies are laid down aroundthe shell during its construction along steered paths such that themagnitude of their respective orientations is less than 45 degrees forregions of φ wherein longitudinal loads incident on the shell exceedcircumferential loads incident on the shell by a selected amount. 36.The aircraft of claim 32, wherein additional longitudinal plies havingorientations in a range of zero degrees, plus or minus 20 degreesrelative to the local fuselage surface axis system are placed in atleast one of a crown and a keel region of the fuselage during itsconstruction for efficiently reacting fuselage bending moments inducedby horizontal tail loads or elevator loads or nosegear slapdown loadsincident thereon.
 37. The aircraft of claim 19, further comprising atleast one additional composite ply layer in a crown region of the shellfor reducing a risk of hail damage in the fuselage crown area.
 38. Theaircraft of claim 19, further comprising at least one additionalcomposite ply layer in a window belt area of upper sides of the shell.39. The fuselage structure of claim 7, wherein a local frame depth ofthe circumferential frames in a crown region of the fuselage isincreased relative to an average frame depth.
 40. The fuselage structureof claim 7, wherein a local frame depth of the circumferential frames ina keel region of the fuselage is increased relative to an average framedepth.
 41. The fuselage structure of claim 7, wherein a local framedepth of the circumferential frames in left and a right side regions ofthe structure in a passenger cabin portion of the structure aredecreased relative to an average frame depth.
 42. The aircraft of claim7, wherein each of the circumferential frames have a varying depth asdefined by an outer edge of the frame lying substantially along a firstelliptical path and an inner edge lying substantially along a secondelliptical path, and wherein the ratio of the major axis to the minoraxis is greater for the second elliptical path than for the firstelliptical path.